Semiconductor devices, in particular, nitride semiconductor devices have been actively developed as high-withstand-voltage, high-power semiconductor devices, by utilizing their characteristics such as a high saturation electron velocity, a wide band gap, and so on. Many reports have been made on field-effect transistors, in particular, HEMTs (High Electron Mobility Transistors) as the nitride semiconductor devices. Especially, an AlGaN/GaN HEMT using GaN as an electron transit layer and using AlGaN as an electron supply layer has been drawing attention. In the AlGaN/GaN HEMT, a distortion resulting from a difference in lattice constant between GaN and AlGaN occurs in AlGaN. Owing to piezoelectric polarization caused by the distortion and to spontaneous polarization of AlGaN, a high-concentration two-dimensional electron gas (2DEG) is obtained. This makes it possible to realize high withstand voltage and high output power.    Patent Document 1: Japanese Laid-open Patent Publication No. 2003-59944    Patent Document 2: Japanese Laid-open Patent Publication No. 2000-100831
For the HEMT, research and development are advanced for a gate electrode which can reduce the gate capacitance and the gate resistance in order to improve the high-frequency characteristics. An HEMT is devised which has a gate electrode in a so-called overhanging shape composed of a narrow fine gate and a wide over gate thereon. In the HEMT, when a high drain voltage is applied, a high electric field is applied around the gate electrode. In particular, very high electric fields concentrate on the fine gate end and the over gate end. This high electric field damages semiconductor crystals at the fine gate end and damages a protective insulating that covers the semiconductor surface at the over gate end. In either case, the high electric field causes deterioration or breakdown of device characteristics, thereby significantly decreasing the reliability of the device.